Abstract <p>The interaction between the electric charges of the electron and hole plays a key role in the formation of a quantum exciton states, their energy spectrum, and the exciton lifetime. In a spatially indirect exciton (IX), in which the electron and hole are separated by a transition layer this interaction directly depends on the geometric parameters of the interface–indirect exciton (IX–interface) system. In this study, the influence of the IX–interface system geometry on the energy spectrum binding of the IX is analytically investigated. It is rigorously demonstrated that the geometric parameters are quantized. The effective permittivity of the interface becomes dependent on the orbital and magnetic quantum numbers of the IX. The IX binding energy has nonlinear dependence of on the geometric parameters. Geometry shapes the fine structures of the IX states, as well as the exciton absorption, reflection, and luminescence spectra of the heterostructure. All these manifestations of geometry are accessible to experimental observation. This allows the use of the IX‒interface geometry for exciton spectroscopy of the interface layer. The geometry can be controlled by polarized light and an electric field. This allows the use of quantum geometric states of IX as qubits. Fine structures of the binding energy spectra of the ground state of IX were modeled for two planar heterostructures, SiO₂/Si₃N₄ and GaAs/CdSe. It should be noted that the obtained conclusions are valid not only for planar layered heterostructures.</p>